The Canadian began the match strongly as she quickly raced into a 3-0 lead courtesy of an early break.
The 21-year-old maintained her intensity to close out the set 6-2 as Hradecka committed a series of unforced errors.
Bouchard dominated the second set as she manoeuvred the Czech around the court with ease, which allowed her to pick her spot with her accurate forehand.
The Canadian held her serve to clinch the second 6-2 and secure the match in just under an hour.
She will now face CoCo Vandeweghe in the third round of the competition.